Definitions and basic results -- Some recently solved problems -- Some (catenary) chain conjectures -- The chain conjecture -- The Depth Conjecture and the weak Depth Conjecture -- The H-conjecture -- The descended GB-conjecture and the GB-conjecture -- The strong avoidance conjecture and the avoidance conjecture -- The upper conjecture -- The taut-level conjecture -- The catenary chain conjecture -- The normal chain conjecture -- Comments on (3.3.1) and conjecture (K) -- Some examples -- Some related questions